WASHINGTON — A growing group of Ted Cruz’s Republican Senate colleagues are infuriated with his tactics.

So frustrated was Arizona Sen. John McCain with the latest, forcing fellow Republicans to take a politically risky vote on lifting the debt ceiling, that Thursday he tweeted a Wall Street Journal editorial accusing the Texas lawmaker of instigating “needless drama that helps to explain why Republicans remain a minority.”

Yet there’s not much McCain, Senate Minority Leader Mitch McConnell or other Republicans can do to change Cruz’s behavior.

“In this day and age, there are no tools available to a leader to punish a member like Sen. Cruz, especially because Sen. Cruz doesn’t care what either the leader or the rest of his caucus thinks,” said Jim Manley, a former top aide to Senate Majority Leader Harry Reid, a Nevada Democrat.

Cruz’s insistence on Wednesday on a 60-vote threshold to advance legislation lifting the nation’s borrowing cap foiled his party leadership’s plan to let the measure move forward with only Democratic votes. He led the October fight to defund the 2010 health-care law, resulting in a partial government shutdown and the party’s cratering in public-opinion polls.

The Republican Party’s favorability was at a record low of 28 percent in a Gallup Poll conducted Oct. 3-6, during the shutdown. That was down 10 percentage points from the previous month and 15 points below Democrats.

In decades past, leaders could rein in such behavior by threatening to take away committee assignments or financial support, or shunning lawmakers. None of those tactics are effective now as campaign cash flows freely from outside the party machinery and cable outlets offer ways to grab attention and influence.

In addition, the potential 2016 presidential aspirant who is aligned with the small-government tea party movement has demonstrated scant interest in cultivating Senate allies or building legislative coalitions, making him even more impervious to pressure from his colleagues.

The risk for Republicans is that Cruz will press similar votes and undermine the party’s ability to win the net six seats needed to gain control of the Senate. Republican infighting has twice, in 2010 and again in 2012, blown up its strategy for retaking the chamber.

McConnell had to vote “yes” on advancing the debt bill to bring along enough fellow Republicans — immediately providing fodder for his Republican opponent in the state’s May 20 primary, Louisville businessman Matt Bevin.

Cruz has maintained close ties to the Senate Conservatives Fund, a political action committee founded by former South Carolina Republican Senator Jim DeMint that has helped to elect tea party-backed senators since 2010 and is targeting McConnell.

The group, which has already spent more than $1 million this cycle, has endorsed Bevin in the Kentucky race and this week aired a Web ad criticizing McConnell’s votes favoring debt-limit increases.